Integration by parts is a good way to approach this one.
\(\displaystyle \int cos(\sqrt{x})dx\)
Let \(\displaystyle v=sin(\sqrt{x}), \;\ du=\frac{1}{\sqrt{x}}dx, \;\ u=2\sqrt{x}, \;\ du=\frac{1}{\sqrt{x}}dx\)
\(\displaystyle 2\sqrt{x}sin(\sqrt{x})-\int\frac{sin(\sqrt{x})}{\sqrt{x}}dx\)
Use a u sub on the integral remaining and finish.
